New Torsional Surface Elastic Waves in Cylindrical Metamaterial Waveguides for Sensing Applications
In this paper, we demonstrate that torsional surface elastic waves can propagate along the curved surface of a metamaterial elastic rod (cylinder) embedded in a conventional elastic medium. The crucial parameter of the metamaterial rod is its elastic compliance <inline-formula><math xmlns=&...
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2024-12-01
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| author | Piotr Kiełczyński Krzysztof Wieja Andrzej Balcerzak |
| author_facet | Piotr Kiełczyński Krzysztof Wieja Andrzej Balcerzak |
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| description | In this paper, we demonstrate that torsional surface elastic waves can propagate along the curved surface of a metamaterial elastic rod (cylinder) embedded in a conventional elastic medium. The crucial parameter of the metamaterial rod is its elastic compliance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mn>44</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced><mo>,</mo></mrow></semantics></math></inline-formula> which varies as a function of frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi></mrow></semantics></math></inline-formula> analogously to the dielectric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced></mrow></semantics></math></inline-formula> in Drude’s model of metals. As a consequence, the elastic compliance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mn>44</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced></mrow></semantics></math></inline-formula> can take negative values <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mn>44</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula> as a function of frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi></mrow></semantics></math></inline-formula>. Negative elastic compliance (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mn>44</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula>) enables the emergence of new surface states, i.e., new types of surface elastic waves. In fact, the proposed torsional elastic surface waves can be considered as an elastic analog of Surface Plasmon Polariton (SPP) electromagnetic (optical) waves propagating along a metallic rod (cylinder) embedded in a dielectric medium. Consequently, we developed the corresponding analytical equations, for the dispersion relation and group velocity of the new torsional elastic surface wave. The newly discovered torsional elastic surface waves exhibit virtually all extraordinary properties of their electromagnetic SPP counterparts, such as strong subwavelength concentration of the wave energy in the vicinity of the cylindrical surface <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi><mo>=</mo><mi>a</mi></mrow></semantics></math></inline-formula>) of the guiding rod, very low phase and group velocities, etc. Therefore, the new torsional elastic surface waves can be used in: (a) near-field subwavelength acoustic imaging (super-resolution), (b) acoustic wave trapping (zero group and phase velocity), etc. Importantly, the newly discovered torsional elastic surface waves can form a basis for the development of a new generation of ultrasonic sensors (e.g., viscosity sensors), biosensors, and chemosensors with a very high mass sensitivity. |
| format | Article |
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| institution | Kabale University |
| issn | 1424-8220 |
| language | English |
| publishDate | 2024-12-01 |
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| spelling | doaj-art-dcf54f21b0754c02b71fd63534489f362025-01-10T13:21:01ZengMDPI AGSensors1424-82202024-12-0125114310.3390/s25010143New Torsional Surface Elastic Waves in Cylindrical Metamaterial Waveguides for Sensing ApplicationsPiotr Kiełczyński0Krzysztof Wieja1Andrzej Balcerzak2Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawińskiego 5B, 02-106 Warsaw, PolandInstitute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawińskiego 5B, 02-106 Warsaw, PolandInstitute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawińskiego 5B, 02-106 Warsaw, PolandIn this paper, we demonstrate that torsional surface elastic waves can propagate along the curved surface of a metamaterial elastic rod (cylinder) embedded in a conventional elastic medium. The crucial parameter of the metamaterial rod is its elastic compliance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mn>44</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced><mo>,</mo></mrow></semantics></math></inline-formula> which varies as a function of frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi></mrow></semantics></math></inline-formula> analogously to the dielectric function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced></mrow></semantics></math></inline-formula> in Drude’s model of metals. As a consequence, the elastic compliance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mn>44</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced></mrow></semantics></math></inline-formula> can take negative values <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mn>44</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula> as a function of frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi></mrow></semantics></math></inline-formula>. Negative elastic compliance (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mn>44</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mfenced separators="|"><mrow><mi>ω</mi></mrow></mfenced><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula>) enables the emergence of new surface states, i.e., new types of surface elastic waves. In fact, the proposed torsional elastic surface waves can be considered as an elastic analog of Surface Plasmon Polariton (SPP) electromagnetic (optical) waves propagating along a metallic rod (cylinder) embedded in a dielectric medium. Consequently, we developed the corresponding analytical equations, for the dispersion relation and group velocity of the new torsional elastic surface wave. The newly discovered torsional elastic surface waves exhibit virtually all extraordinary properties of their electromagnetic SPP counterparts, such as strong subwavelength concentration of the wave energy in the vicinity of the cylindrical surface <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi><mo>=</mo><mi>a</mi></mrow></semantics></math></inline-formula>) of the guiding rod, very low phase and group velocities, etc. Therefore, the new torsional elastic surface waves can be used in: (a) near-field subwavelength acoustic imaging (super-resolution), (b) acoustic wave trapping (zero group and phase velocity), etc. Importantly, the newly discovered torsional elastic surface waves can form a basis for the development of a new generation of ultrasonic sensors (e.g., viscosity sensors), biosensors, and chemosensors with a very high mass sensitivity.https://www.mdpi.com/1424-8220/25/1/143torsional elastic waveselastic metamaterialsnegative elastic compliancedispersion curvesphase velocitygroup velocity |
| spellingShingle | Piotr Kiełczyński Krzysztof Wieja Andrzej Balcerzak New Torsional Surface Elastic Waves in Cylindrical Metamaterial Waveguides for Sensing Applications Sensors torsional elastic waves elastic metamaterials negative elastic compliance dispersion curves phase velocity group velocity |
| title | New Torsional Surface Elastic Waves in Cylindrical Metamaterial Waveguides for Sensing Applications |
| title_full | New Torsional Surface Elastic Waves in Cylindrical Metamaterial Waveguides for Sensing Applications |
| title_fullStr | New Torsional Surface Elastic Waves in Cylindrical Metamaterial Waveguides for Sensing Applications |
| title_full_unstemmed | New Torsional Surface Elastic Waves in Cylindrical Metamaterial Waveguides for Sensing Applications |
| title_short | New Torsional Surface Elastic Waves in Cylindrical Metamaterial Waveguides for Sensing Applications |
| title_sort | new torsional surface elastic waves in cylindrical metamaterial waveguides for sensing applications |
| topic | torsional elastic waves elastic metamaterials negative elastic compliance dispersion curves phase velocity group velocity |
| url | https://www.mdpi.com/1424-8220/25/1/143 |
| work_keys_str_mv | AT piotrkiełczynski newtorsionalsurfaceelasticwavesincylindricalmetamaterialwaveguidesforsensingapplications AT krzysztofwieja newtorsionalsurfaceelasticwavesincylindricalmetamaterialwaveguidesforsensingapplications AT andrzejbalcerzak newtorsionalsurfaceelasticwavesincylindricalmetamaterialwaveguidesforsensingapplications |